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A NOTE ON THE STABILITY OF ACCELERATED MOTIONS

When the directional stability of a ship or any other sea going vessel is investigated, it is usually assumed that the vessel has an initial constant forward reference motion. This assumption is relaxed in the note, the vessel being considered to have instead an accelerating or decelerating motion straight ahead. To permit this it is necessary to adopt some simplifying assumptions and those adopted have been employed previously for ships even though they are known not to be strictly valid; in particular, the hydrodynamic actions are expressed in terms of slow motion derivatives which are assumed to be constant and independent of forward speed in their dimensional form. The analysis suggests that criteria of directional stability which are relevant to a steady reference motion do not necessarily apply if the reference motion is not constant.